TY - GEN

T1 - What is a natural notion of distance between power spectral density functions?

AU - Georgiou, Tryphon T.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - We introduce a Riemannian metric on the cone of spectral density functions of discrete-time random processes. This is motivated by a problem in prediction theory, and it is analogous to the Fisher information metric on simplices of probability density functions. Interestingly, in either metric, geodesics and geodesic distances can be characterized in closed form. The goal of this paper is to highlight analogies and differences between the proposed differential-geometric structure of spectral density functions and the information geometry of the Fisher metric, and raise the question as to what a natural notion of distance between power spectral density functions is.

AB - We introduce a Riemannian metric on the cone of spectral density functions of discrete-time random processes. This is motivated by a problem in prediction theory, and it is analogous to the Fisher information metric on simplices of probability density functions. Interestingly, in either metric, geodesics and geodesic distances can be characterized in closed form. The goal of this paper is to highlight analogies and differences between the proposed differential-geometric structure of spectral density functions and the information geometry of the Fisher metric, and raise the question as to what a natural notion of distance between power spectral density functions is.

KW - Spectral geometry

KW - information geometry

UR - http://www.scopus.com/inward/record.url?scp=84927728841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927728841&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84927728841

T3 - 2007 European Control Conference, ECC 2007

SP - 358

EP - 361

BT - 2007 European Control Conference, ECC 2007

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2007 9th European Control Conference, ECC 2007

Y2 - 2 July 2007 through 5 July 2007

ER -